Au ultraprecision grinder is developed which can grind hard and brittle materials such as silicon, glass and ceramics by a cup-type grinding wheel. It has the following characteristics; (1)It is relatively small and stiff because the grinding wheel spindle and workpiece spindle are set horizontally. (2)A fine and coarse positioning device can give very low speed of 1∿100nm/s to the workpiece spindle after a high speed greater than 100nm/s under the feedback control of the workpiece spindle. The results are; (i) For the silicon wafer of 150mm diameter, the surface roughness of 4nm Ry and flatness of 0.2μm can be obtained by partially ductile mode process. (ii) For the ferrite and alumina the surface roughness of 2∿4μm Ry can be obtained by perfect ductile mode process.